//请实现一个函数用来判断字符串是否表示数值（包括整数和小数）。例如，字符串"+100"、"5e2"、"-123"、"3.1416"、"-1E-16"、"012
//3"都表示数值，但"12e"、"1a3.14"、"1.2.3"、"+-5"及"12e+5.4"都不是。 
//
// 
// Related Topics 数学 
// 👍 137 👎 0
#include <iostream>
#include <string>
#include <stack>
#include <unordered_map>
#include <vector>uio
using namespace std;

//leetcode submit region begin(Prohibit modification and deletion)
class Solution {
public:
    enum State{
        STATE_INITIAL,
        STATE_INT_SIGN,
        STATE_INTEGER,
        STATE_POINT,
        STATE_POINT_WITHOUT_INT,
        STATE_FRACTION,
        STATE_EXP,
        STATE_EXP_SIGN,
        STATE_EXP_NUMBER,
        STATE_END,
    };
    enum CharType {
        CHAR_NUMBER,
        CHAR_EXP,
        CHAR_POINT,
        CHAR_SIGN,
        CHAR_SPACE,
        CHAR_ILLEGAL,
    };
    CharType toCharType(char ch){
        if (ch >= '0' && ch <= '9'){
            return CHAR_NUMBER;
        } else if (ch == 'e' || ch == 'E'){
            return CHAR_EXP;
        } else if (ch == '.'){
            return CHAR_POINT;
        } else if (ch == '+' || ch == '-'){
            return CHAR_SIGN;
        } else if (ch == ' '){
            return CHAR_SPACE;
        } else {
            return CHAR_ILLEGAL;
        }
    }
    bool isNumber(string s) {
        unordered_map<State,unordered_map<CharType,State>> transfer{
                {
                    STATE_INITIAL,{
                        {CHAR_SPACE, STATE_INITIAL},
                        {CHAR_NUMBER, STATE_INTEGER},
                        {CHAR_POINT, STATE_POINT_WITHOUT_INT},
                        {CHAR_SIGN, STATE_INT_SIGN},
                    }
                },{
                        STATE_POINT_WITHOUT_INT, {
                            {CHAR_NUMBER, STATE_FRACTION},
                        }
                }, {
                        STATE_FRACTION,{
                            {CHAR_NUMBER, STATE_FRACTION},
                            {CHAR_EXP, STATE_EXP},
                            {CHAR_SPACE, STATE_END},
                        }
                }, {
                        STATE_EXP,{
                            {CHAR_NUMBER, STATE_EXP_NUMBER},
                            {CHAR_SIGN, STATE_EXP_SIGN},
                        }
                }, {
                        STATE_EXP_SIGN, {
                            {CHAR_NUMBER, STATE_EXP_NUMBER},
                        }
                }, {
                        STATE_EXP_NUMBER, {
                            {CHAR_NUMBER, STATE_EXP_NUMBER},
                            {CHAR_SPACE, STATE_END},
                        }
                }, {
                        STATE_END, {
                            {CHAR_SPACE, STATE_END},
                        }
                }
        };

        int len = s.length();
        State st = STATE_INITIAL;

        for (int i = 0; i < len; ++i) {
           CharType type =  toCharType(s[i]);
           if (transfer[st].find(type) == transfer[st].end()){
               return false;
           } else{
               st = transfer[st][type];
           }
        }
        return st == STATE_INTEGER || st == STATE_POINT || st == STATE_FRACTION || st == STATE_EXP_NUMBER || st == STATE_END;
    }
};
//leetcode submit region end(Prohibit modification and deletion)
